Principal component analysis and perturbation theory–based robust damage detection of multifunctional aircraft structure

A fundamental problem in structural damage detection is to define an efficient feature to calculate a damage index. Furthermore, due to perturbations from various sources, we also need to define a rigorous threshold whose overtaking indicates the presence of damages. In this article, we develop a robust damage detection methodology based on principal component analysis. We first present an original damage index based on projection of the separation matrix, and then, we drive a novel adaptive threshold that does not rely on statistical assumptions. This threshold is analytic, and it is based on matrix perturbation theory. The efficiency of the method is illustrated using simulations of a composite smart structure and experimental results performed on a conformal load-bearing antenna structure laboratory test

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator

Output tracking control for class of fuzzy time-delay systems

Dimirovski, Georgi M. (Dogus Author)The output tracking control problem for fuzzy time-delay systems in presence of parameter perturbations has been solved via fuzzy T-S system models and variable-structure control approach. Following the reaching condition, a variable-structure fuzzy control method is proposed accordingly, when the time delay is known and available and when unknown and unavailable. The method guarantees the system operation arrives to the sliding surface in finite time interval and be kept there thereafter while tracking the desired trajectory. The sufficient condition for globally bounded state is derived by using the ISS theory and the LMI method. A simulation example demonstrates the validity and effectiveness of the proposed method.16th Triennial World Congress of International, Federation of Automatic Control, IFAC 200

Numerical simulation on a fixed mesh for the feedback stabilization of a fluid–structure interaction system with a structure given by a finite number of parameters

We study the numerical approximation of a 2d fluid–structure interaction problem stabilizing the fluid flow around an unstable stationary solution in presence of boundary perturbations. The structure is governed by a finite number of parameters and a feedback control law acts on their accelerations. The existence of strong solutions and the stabilization of this fluid–structure system were recently studied in [3]. The present work is dedicated to the numerical simulation of the problem using a fictitious domain method based on extended Finite Element [4]. The originality of the present work is to propose efficient numerical tools that can be extended in a simple manner to any fluid-structure control simulation. Numerical tests are given and the stabilization at an exponential decay rate is observed for small enough initial perturbations

Construction of stochastic differential equations of motion in canonical variables

Galiullin proposed a classification of inverse problems of dynamics for the class of ordinary differential equations (ODE). Considered problem belongs to the first type of inverse problems of dynamics (of the three main types of inverse problems of dynamics): the main inverse problem under the additional assumption of the presence of random perturbations. In this paper Hamilton and Birkhoff equations are constructed according to the given properties of motion in the presence of random perturbations from the class of processes with independent increments. The obtained necessary and sufficient conditions for the solvability of the problem of constructing stochastic differential equations of both Hamiltonian and Birkhoffian structure by the given properties of motion are illustrated by the example of the motion of an artificial Earth satellite under the action of gravitational and aerodynamic forces

Construction of stochastic differential equations of motion in canonical variables

Galiullin proposed a classification of inverse problems of dynamics for the class of ordinary differential equations (ODE). Considered problem belongs to the first type of inverse problems of dynamics (of the three main types of inverse problems of dynamics): the main inverse problem under the additional assumption of the presence of random perturbations. In this paper Hamilton and Birkhoff equations are constructed according to the given properties of motion in the presence of random perturbations from the class of processes with independent increments. The obtained necessary and sufficient conditions for the solvability of the problem of constructing stochastic differential equations of both Hamiltonian and Birkhoffian structure by the given properties of motion are illustrated by the example of the motion of an artificial Earth satellite under the action of gravitational and aerodynamic forces